The International Automobile Federation (FIA) said in a statement that a notification of charges against both parties had been sent to the president of the tribunal.
"Pirelli and Mercedes AMG Petronas F1 Team have been convened by the President of the International Tribunal to appear before a judging panel of the International Tribunal," it added.
The verdict will be published 'as soon as possible' after the hearing.
Mercedes, who finished third in Sunday's Canadian Grand Prix with 2008 world champion Lewis Hamilton, risk stiff sanctions ranging from a fine to points deduction or even exclusion if found guilty.
The rules bar teams from testing during the season with a current car.
Champions Red Bull and Ferrari, the sport's most successful team, made formal protests at last month's Monaco Grand Prix when news of the test leaked out.
Mercedes used their 2013 car at the 'secret' test in Barcelona, which came just before Germany's Nico Rosberg won in Monaco for the team, but have said the move was approved by the governing body.
They have also argued that the test was private and not secret, run and organised by Pirelli - who are sole providers rather than 'competitors' in the championship and therefore not subject to the ban that applies to teams.
Mercedes said last week that they welcomed the chance to present their case to the tribunal and would explain the full facts in "an open and transparent manner".
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